Pion charge form factor and constraints from space-time translations

TL;DR

This paper examines how Poincaré covariant space-time translations affect the calculation of the pion charge form factor in relativistic quantum mechanics, highlighting constraints and approach equivalences.

Contribution

It demonstrates the general inconsistency of single-particle current assumptions with space-time translation constraints, except in the front-form with $q^+=0$, and discusses approach restoration.

Findings

Constraints challenge single-particle current assumption

Front-form with $q^+=0$ satisfies constraints

Approach equivalence can be restored

Abstract

The role of Poincar\'e covariant space-time translations is investigated in the case of a relativistic quantum mechanics approach to the pion charge form factor. It is shown that the related constraints are generally inconsistent with the assumption of a single-particle current, which is most often referred to. The only exception is the front-form approach with $q^+=0$. How accounting for the related constraints, as well as restoring the equivalence of different RQM approaches in estimating form factors, is discussed. Some extensions of this work and, in particular, the relationship with a dispersion-relation approach, are presented. Conclusions relative to the underlying dynamics are given.